(I see an error I made, but I'd still like to know if there is a specific order.)
I have here $\left(6^{-36}\right)/\left(6^{-16}\right)\cdot\left(6^{16}\right)$.
If I do the division first, it's $-36$ minus $-16$, making an addition of plus $16$ for $6^{-20}$.
This times the $6^{16}$ equals $6^{-4}$.
But if I do the multiplication first, the powers of $16$ and $-16$ cancel out, leaving me with $6^{-36}$, which is a radically different answer.
When it comes to exponents, do I have to strictly go from left to right first, in terms of division/multiplication?
Evaluating $a/b\cdot c$ requires a bracketing convention. On BODMAS we divide first, giving $(a/b)c=ac/b$. On PEMDAS we multiply first, giving $a/(bc)$.